Coherence is a property of waves, such as those in the electromagnetic spectrum, in which light is a subset. The property of coherence enables two waves to exhibit interference. When waves interfere, parts of the waves may add constructively or subtract destructively. Coherence, or the degree of coherence, is a parameter that quantifies the ability of the two waves to interfere with each another. The property of coherence is used in various applications such as interferometry, positioning, optical testing, holography, optical strain sensors, radio antenna arrays, optical tomography, telescope interferometers, radio astronomy and many other optical and radio frequency (RF) applications.
In addition to coherence relating to the ability of two waves to interfere, coherence may also relate to one wave's ability to interfere with itself. More specifically, the degree of coherence of a wave can imply how much a wave is like a copy of itself shifted slightly in time or space. For example, any wave is perfectly identical to a copy of itself that is not shifted. However, shifting the copy of the wave a small amount might cause the copy to appear nothing like the original wave. Such a wave has a lower degree of coherence than a wave that can be shifted by a larger amount and still be similar to itself. So the higher the degree of coherence, the more self-similar the wave is. In other words, the wave has a higher autocorrelation, since it correlates more strongly with itself.
Electromagnetic waves, such as light or RF waves, have a constant speed of propagation represented by the symbol “c” which is approximately 300,000,000 meters per second in vacuum. Since the speed is constant, an electromagnetic wave can be counted on to move a specific distance when a specific amount of time passes. Also, a specific amount of time passes when an electromagnetic wave moves a specific distance. As such, shifting, or moving, an electromagnetic wave can be described as a change in time or a change in distance. These descriptions (temporal and spatial) can generally be used interchangeably as the speed of propagation “c” can be used to convert between the time and the distance.
Any wave will correlate perfectly to a copy of itself that is not shifted. A slightly coherent wave will also correlate somewhat with a slightly shifted copy of itself, but will likely not correlate at all with a copy of itself that is shifted a large amount. In contrast, a perfectly coherent wave will correlate perfectly with a copy of itself that is shifted by any amount. A wave that can be transversely shifted a large amount and remain correlated to itself is said to have high spatial coherence, whereas a wave that can be longitudinally shifted a large amount and remain correlated to itself is said to have high temporal coherence. Temporal coherence can be quantified by the coherence length or the coherence time, which is the coherence length divided by “c”.
The spectral content of a signal, or a wave, can be considered from a “frequency domain” point of view. Such a frequency domain view can be obtained by performing the Fourier transform of the time-domain representation of the signal. The bandwidth of the signal is the span of frequencies over which its spectral content is non-zero. For example, lasers generally have a very narrow bandwidth. A theoretically perfect laser might have only one frequency component, and thus an infinitesimally small bandwidth. The frequency domain view of the signal from such a perfect laser would appear as a single line at the frequency of the laser. This line can be represented mathematically by the delta function. Accordingly, such a source of electromagnetic energy can be referred to as a line source. In contrast, white light is composed of a broad range of frequencies that are visible to the human eye. That is, white light has many frequency components, and thus a wide bandwidth. A source of white light, far from being a line source, is instead a broadband, or wideband, source.
Since a laser can emit a (very nearly) single frequency of radiation, the light is monochromatic, or generally always the same, or highly self-similar. Thus, laser light can be very coherent. In other words, laser light can have a very long coherence length. For example, a frequency stabilized helium-neon (HeNe) laser can produce light with coherence lengths of several kilometers. In contrast, white light is made up of many different frequencies. With such great diversity of spectral content, a wave from a white light source may not be very similar if examined at different times or places along the wave. That is, the wave is not highly self-similar, not very coherent, and may have an extremely short coherence length. With such a short coherence length, the white light wave will only interfere with a copy of itself that is very minimally shifted in time or space.
Interferometry is a technique where interference between two or more waves creates an interference pattern that can be analyzed to determine differences between the waves. Interferometry is often used for measuring small path length differences such as would occur from small distance or refractive-index differences. One or more interference patterns are typically processed to extract phase maps or other useful data. Interferometers often use two waves having the same frequency. This can be accomplished by splitting a single source into two, in which case each of the splits might be called a leg or branch of the interferometer. Where the two waves are in phase, they will interfere constructively (add to each other), while where they are out of phase, they will interfere destructively (cancel each other out). Thus the constructive or destructive interferences shown within the interference pattern can indicate differences in the path lengths between the arms of the interferometer. There are many types of interferometers all of which employ the same basic principles. Some examples include the Michelson interferometer, the Twyman-Green interferometer, the Mach-Zehnder interferometer, the Sagnac interferometer, and the Fabry-Perot interferometer.
It is often desirable for the interference pattern of interest to have the highest contrast possible. This occurs when regions of destructive interference produce nearly complete cancellation of the waves, and regions of constructive interference have the greatest wave amplitude. In the past, this has typically meant that the path length difference between the two paths of interest would have to be much smaller than the coherence length of the source. So, for example, if a white-light source is used, its extremely short coherence length necessitates that the interferometer's two path lengths would have to be almost exactly the same.
In an interferometer setup there are generally many surfaces within the system off of which the waves may reflect or scatter creating wave paths in addition to those of the main interfering legs. Although these are not the main interfering wave paths, they can still introduce extraneous interference patterns if their path length differences are shorter than the source's coherence length. These extraneous patterns can mix with the desired interference pattern, making the resulting pattern more difficult to process, thereby reducing the effectiveness of the interferometer. Various techniques may be used to attempt to mitigate the occurrence of these extraneous fringe patterns, including the use of: wedged optics, anti-reflection coatings, field stops, software processing, phase shifting, polarization adjustment, and other methods. These techniques may be difficult to employ, expensive, and/or have limited efficacy.
It is with respect to these considerations and others that the disclosure made herein is presented.